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This problem trains for: SAT-I, CAHSEE, GMAT, Math Kangaroo 7-8.

Human activities add almost 1.4 metric tons of carbon per person per year to the worldwide airborne carbon. Before the Industrial Revolution, the concentration of carbon dioxide in the atmosphere was about 280 parts per million. By 1958, the concentration of carbon dioxide had increased by about 12.5% and by 2007 it had increased by another 21.6%. What was the overall percent increase from before the Industrial Revolution to 2007?

(based on information provided by NASA)

The overall percent increase can be calculated rapidly as follows:

If this quick computation is a mystery to you, here is a step-by-step explanation:

Compute the final concentration by applying successively the two increases:

And then apply the formula for computing the percent change given the initial and the final amounts:

If we do not go ahead to perform the partial computations, we can see how the initial amount simplifies and we get the faster procedure: